Chapter 12 - Functions of Several Veriables - 12.7 Tangent Planes and Linear Approximation - 12.7 Exercises - Page 935: 8

$$dw = {f_x}\left( {a,b,c} \right)dx + {f_y}\left( {a,b,c} \right)dy + {f_z}\left( {a,b,c} \right)dz$$

$$\eqalign{ & {\text{If }}f\left( {x,y,z} \right){\text{ is differentiable at }}\left( {a,b,c} \right){\text{ with }}w = f\left( {x,y,z} \right),{\text{ so}} \cr & dw = {f_x}\left( {a,b,c} \right)dx + {f_y}\left( {a,b,c} \right)dy + {f_z}\left( {a,b,c} \right)dz \cr & \left( {{\text{See page 934}}} \right) \cr} $$